1 design matrix intrinsic correlations and non-sphericity correction intrinsic correlations and...
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1
Design MatrixDesign Matrix
intrinsic correlations andnon-sphericity correction
intrinsic correlations andnon-sphericity correction
filterfilter
DataData
SPM{T}SPM{T}
The General Linear Model
vT
T
T
TcV
c
SYSX
SSVN
SSXSY
XY
~}ˆ{ˆ
ˆ
)(ˆ
,),0{~ 2
adjustmentXX
none
whitening
S
001
1
21
}{
){
}{ˆ
)(1
)()(ˆ}ˆ{ˆ
2
2
2
RVRVtrace
RVtracev
RVtrace
RYY
SXSXR
cSXVSXccV
T
TTT
contrast images
contrast images
2
SPM{T}SPM{T}
speed
isoluminant stimuli (even)
isochromatic stimuli (odd)V5V5
3
Design matrix1 2 3 4
100
200
300
contrast
z = 3mm
SPM{T} PPM
z = 3mm
4
Basis functions
Single HRF
FIR model
Temporal basis functions
i
ii ttuty
ttth
)()(
)()()( 2211
)()(
)()(
tuTty
uTth
))(()(
)()()( 2211
iii tuTty
tTtTth
Stimulus function
)(uTi
)(uT
)( it
)(tuTi
Design matrixDesign matrix
SPM{F}SPM{F}
)(tu
5
sf
tionflow induc
v,q y
)(tu
s
v
f
hidden states
neuronal input
BOLD response
v
q
},,,{ qvfs
q/vvf,Efqτ /α
dHbchanges in
1)( /αvfvτ
volumechanges in
1
f
q
)1( fγsus
ignalependent sactivity-d
hemodynamicshemodynamics
6
Nonlinear saturation
7
V1 IFG
V5
SPC
Motion
Photic
Attention
..82(100%)
.42(100%)
.37(90%)
.69 (100%)
.47(100%)
.65 (100%)
.52 (98%)
.56(99%)
8
spiny stellate
cells
inhibitory interneurons
pyramidal cells
4 3
236
746
63
225
1205
52
650
214
014
41
278
038
87
2)(
2))()()((
2))()((
2))()((
iii
i
ee
LB
e
e
ee
LF
e
e
ee
LB
e
e
xxxS
Hx
xx
xxxSxSAA
Hx
xx
xxx
xxCuxSIAA
Hx
xx
xxxSIAA
Hx
xx
1 2)( 0xSAF
)( 0xSAL
)( 0xSAB
Extrinsicforward
connections
Extrinsic backward connections
Intrinsic connections
Neuronal model
Extrinsic lateral connections
9
spiny stellate
cells
inhibitory interneurons
pyramidal cells
IntrinsicForward
BackwardLateral time
input
.56
/.6
1
.59
/.8
7
.05
/.0
4
.00/.09
.01/3.68
P300 Real andmodelled
frequentrare
Time {s}
Time {s}